For the link via the \({m_k}\) th element at the \(k\) th IRS, the reflection channel consists of three parts, namely, the BS-IRS link \({u_{k,{m_k}}}\) , the IRS phase shift \({\varphi _{k,{m_k}}}\)  and the IRS-user link \(v_{k,{m_k}}^ * \) , where \({\varphi _{k,{m_k}}}\)  can be configured by the IRS controller to facilitate the coherent superposition of different reflection links. Nonetheless, the configuration of \({\varphi _{k,{m_k}}}\)  needs the prior knowledge of the instantaneous CSI, i.e., \({u_{k,{m_k}}}\) , \(v_{k,{m_k}}^ * \) , which, as stated earlier, is challenging to be obtained separately due to the deficiency of baseband signal processing capability at the IRS. To solve this problem, some novel channel estimation methods have been proposed to estimate the cascaded reflection links instead [1]}, [2]}, [3]}, [4]}. Therefore, (REF ) can be rewritten as
\(r = \left( {\sum \limits _{k = 1}^K {\sum \limits _{{m_k} = 1}^{{M_k}} {{\varphi _{k,{m_k}}}{h_{k,{m_k}}}} } } \right)\sqrt{q} s + n,\) 
